Question: Rewrite as a simplified fraction. ${0.81\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 816.6666...\\ 100x &= 81.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 735}$ ${x = \dfrac{735}{900}} $ ${x = \dfrac{49}{60}} $